Answer:
100° and 80°
Step-by-step explanation:
Ratio means they are sort of multiples of a certain number (which I used X) and A is 5 times X and B is 4 times X. Since they are supplementary they sum 180°. After summing up both angles and equaling them to 180°, solve for X and substitute in the original equations
Answer: First option is correct.
Step-by-step explanation:
A number in an expression is a term that contains no variables.
So, it is known as constant term.
if any term is with variable or variables, then it can't be consider as a number.
Then, it becomes only a term.
But if there is no variables in a term is present, then it is called to be number.
Hence, First option is correct.
the profit is a polynomial function :
p(x) = x^4 − x^3 − 24
the average profit per unit of product sold is :
ap(x) = (x^4 − x^3 − 24)/(x+2)
now,
(-2) is an "obvious" zero of p(x)
therefore : p(x) is dividable by (x+2)
and
the long division of p(x) by (x+2) gives :
Answer:
ap(x) = x^3 - 3x^2 + 6x - 12
<span>For this case we have the following expression:
</span>
![\frac{n ^ 4-11n ^ 2 + 30}{ n ^ 4-7n ^ 2 + 10} ](https://tex.z-dn.net/?f=%20%5Cfrac%7Bn%20%5E%204-11n%20%5E%202%20%2B%2030%7D%7B%20n%20%5E%204-7n%20%5E%202%20%2B%2010%7D%20%0A%0A)
<span> We are going to make the following change of variables:
</span>
![x = n ^ 2 ](https://tex.z-dn.net/?f=x%20%3D%20n%20%5E%202%0A)
<span>Rewriting the expression we have:
</span>
![\frac{(x ^ 2-11x + 30)}{(x ^ 2-7x + 10)} ](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28x%20%5E%202-11x%20%2B%2030%29%7D%7B%28x%20%5E%202-7x%20%2B%2010%29%7D%20%0A%0A)
<span>Factoring the expression we have:
</span>
![\frac{(x-5) (x-6)}{(x-5) (x-6)} ](https://tex.z-dn.net/?f=%20%5Cfrac%7B%28x-5%29%20%28x-6%29%7D%7B%28x-5%29%20%28x-6%29%7D%20%0A)
<span>Canceling similar terms we have:
</span>
![\frac{x-6}{x-2} ](https://tex.z-dn.net/?f=%20%5Cfrac%7Bx-6%7D%7Bx-2%7D%20%0A)
<span>Returning the change we have:
</span>
![\frac{n ^ 2-6}{n ^ 2-2} ](https://tex.z-dn.net/?f=%20%5Cfrac%7Bn%20%5E%202-6%7D%7Bn%20%5E%202-2%7D%20%0A%0A)
<span> The resctrictions of the function are those that make the denominator equal to zero.
We have then:
</span>
![n ^ 2-2 = 0 n = +/- \sqrt{2} ](https://tex.z-dn.net/?f=n%20%5E%202-2%20%3D%200%0A%0An%20%3D%20%2B%2F-%20%20%5Csqrt%7B2%7D%20%0A)
<span>
Answer: The simplified expression is: </span>
<span>
The restrictions are: </span>